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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Did you know that two fractions can look completely different, but actually be the same? In this lesson, we'll learn about equivalent fractions. We'll also learn to simplify fraction notation.

We're going to learn about equivalent fractions, so let's talk pizza. Your friends Max and Daisy are each offering to share their pizza with you. Max says you can have 2 slices of pizza. Daisy says you can have 4 slices of hers.

Max and Daisy are trying to buy your friendship with pizza. There are worse ways, sure. But who is offering the better deal? Max's pizza only has 4 slices. So he's offering you 2/4 of his pizza. That's a fraction. Daisy's pizza has 8 slices. So, she's offering you 4/8 of her pizza.

2/4 and 4/8. When you put them next to each other, it looks like the same amount either way, right? And, in fact, it is. 2/4 and 4/8 are **equivalent fractions**. These are fractions with the same value.

We can see it in pizza form, but, well, while we're talking about this I kind of ate most of the pizza. Sorry about that. But can we understand it in math terms?

Let's multiply 2/4 by 2/2. 2 * 2 is 4 and 4 * 2 is 8. So, now we have 4/8. Now, why could we do that? Well, 2/2 is the same as 1. If you have one pizza and you multiply it by 1, sadly, you still only have one pizza.

With fractions, we can multiply them by any version of 1, like 2/2, 3/3, 847/847, and the new fraction will look different, but it will be equivalent to our original fraction. So, Daisy wasn't offering us more pizza; she just cut hers into smaller pieces.

You might see an equivalent fraction problem that looks like this: 7/8 = *x*/40. We want to solve for *x*, and there are a few ways we do this.

First, remember that our second fraction must be 7/8 * 1. We just need to figure out what fraction is used. Well, 8 times what is 40? 8 * 5 is 40. So, it must be 5/5. To find *x*, we just multiply 7 * 5. That's 35. So, 7/8 = 35/40. And that's it!

Also, a 40-slice pizza? That's a big pizza, or little slices. If Daisy said she'd give you 35 slices, but they're all the size of a pepperoni slice, well, I guess that's still a lot of pizza.

Anyway, we could also solve this problem by cross multiplying. We could do 7 * 40 = 8*x*. 7 * 40 is 280. 280 / 8 is 35. Again, 35 tiny pizza slices.

Equivalent fractions aren't always about making fractions bigger through multiplication; sometimes we need division. Look at this one: 3/9 = *x*/3.

This time, we want to make the fraction smaller. Let's use a number line to visualize this. Here's what 3/9 looks like. We have a bar divided into 9 segments and 3 are highlighted.

Here's an equivalent bar with just 3 segments.

In that problem, we simplified our fraction notation. The term **fraction notation** just means a fraction written as *a*/*b*. Simplifying fraction notation is when we reduce a fraction to its smallest form.

We can simplify fraction notation in two ways. Let's say we have 24/36. We can just start dividing by numbers that divide cleanly. Let's divide by 2. 24 / 2 is 12. 36 / 2 is 18. Okay, 12/18.

Let's divide by 2 again. We get 6/9. We can't divide by 2 again, but we can divide by 3. 6/9 becomes 2/3. So, 24/36 simplifies to 2/3.

Another method is to find the greatest common factor. That's not like pepperoni being the greatest pizza topping, which is totally not up for debate. It's the largest number that goes into both the numerator and denominator. Let's try that with this one: 42/60.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. We know 21 and 42 won't go into 60. What about 14? No, but 15 does. Is that close enough? No. 7 doesn't go into 60, but 6 does!

So 6 is the greatest common factor of 42 and 60. And what's 42 / 6? 7. And 60 / 6? 10. So 42/60 simplifies to 7/10.

To summarize, we learned about **equivalent fractions**. These are fractions that look different but have the same value. Equivalent fractions are just fractions multiplied or divided by some version of 1. To find a missing number, you can either figure out what the factor is or cross multiply.

When we want to simplify **fraction notation**, or a fraction written as *a*/*b*, we can divide until we can't go any further. Or, we can find the greatest common factor and divide by that. In the end, we have nice and tidy fractions.

By the end of this lesson you should be able to:

- Compare fractions and identify equivalent fractions
- Create equivalent fractions
- Explain what fraction notation is
- Reduce fractions by finding the greatest common factor

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is Factoring in Algebra? - Definition & Example 5:32
- How to Find the Prime Factorization of a Number 5:36
- Using Prime Factorizations to Find the Least Common Multiples 7:28
- Equivalent Expressions and Fraction Notation 5:46
- Factoring Out Variables: Instructions & Examples 6:46
- Combining Numbers and Variables When Factoring 6:35
- Transforming Factoring Into A Division Problem 5:11
- Factoring By Grouping: Steps, Verification & Examples 7:46
- Go to High School Algebra: Factoring

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